Consider a population of individuals in some habitat. When the existence of this population in the habitat is damaging in some sense, one is faced with the problem of controlling the growth of the population within that habitat. Such control action involves cost due to labour, materials, risk, etc. and it is therefore necessary to weigh the damage done by the 'pests' against the cost of the control action and so choose a suitable level at which to apply the control. The amount of damage done by the pest population at any time generally depends on the size of the population at that time, which in turn depends on the initial number of pests, their birth and death rates, and their rates of migration to and from the habitat. These factors are therefore aimed at in any control of the pest population. In particular, pests in a field might be destroying a crop and the control action might consist of treating the field or part of it with chemicals, fencing, spraying the crop, or some other means of 'removing' the pests. The cost is the sum of that due to the loss of crop and that due to the labour and materials of the control action. Alternatively, the pests may be intermediate vectors in the spread of an epidemic, e.g. mosquitoes spreading malaria, in which case the habitat is that in which the susceptibles abide, and the possible control actions are similar to the above, i.e. spraying with insecticides, etc. In an epidemic spread by the infectives or carriers in a large population, the 'pests' are the infectives or carriers, and the control might be to increase the rate of removal of infectives or to inoculate part of the population. The damage due to the epidemic involves a cost when the disease causes the death of hosts or stops hosts from being productive for any period of time. For human hosts, assessing the cost of permanent physical damage, including death, poses ethical problems, but unfortunately these often need to be faced. On the